Technically an air lift pump is a simple design without moving parts. However, it has some big disadvantages.
The first is that the overall efficiency of pump and compressor is very low. The efficiency of the air lift pump itself is about 50 % but the efficiency of the compressor is even lower because a lot of heat is generated during compression.
The second is that you need a well which is much deeper than the water level. This is because the air has to be inserted far below the water level to make that the pressure in the rising main at the point of insertion is less than the pressure in the well at the chosen water depth. If the height in between the water level and the reservoir is 10 m, the point of insertion of the air must lie about 10 m below the water level to get an acceptable pump efficiency. For this condition, the average density of the mixture of water and air bubbles is about half the density of water.
The third is that a 1-cylinder compressor has a very large peak torque. So you need a windmill rotor with a very high starting torque to get an acceptable starting wind speed. Another option is to open a valve in the compressor at low rotational speeds to make that the compressor runs about unloaded at low wind speeds but this needs a mechanism which opens and closes the valve at the correct rotational speeds.
When I was working at the Wind Energy Group of the University of Technology Eindhoven, I have guided a student who has spent four months to investigate the windmill driven air lift pump. The result of this study is given in report R 727 A but this report is in Dutch and no longer available. An air lift pump is only an acceptable option if you need only a little amount of water a day like for drinking water. For irrigation or drainage, the low overall efficiency will result in a very large rotor diameter for the wanted flow.